the difference between 2 numbers, a and b is 21. the difference of 5 times a and 2 times b is 18. What are the values of a and b?

Answer:

233.35488 km (Rounded to 233 km)

Step-by-step explanation:

If you convert miles to kilometers then you would use this conversion factor:

1 mile = 1.609344 km (or 1.61 km)

so in this case,

145 mile = 1.609344 km x 145

145 mile = 233.35488 km

I could also round it to 233 km.

Since your on a trip... i hope u enjoy ur journey to Las Vegas!

Using the formula for the distance between two points, the length of the line segment PQ is of 30 units.

Suppose that we have two points, [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex]. The distance between them is given by:

[tex]D = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

The coordinates of the endpoints for this problem are given by:

Hence the distance is given by:

D = sqrt[(-20 -10)² + (10 - 10)] = 30 units.

More can be learned about the distance between two points at https://brainly.com/question/18345417

#SPJ1

Answer: 30 units

Step-by-step explanation:

Answer:

11

Step-by-step explanation:

9 + 12 + 7 + 13 + 21 + 10 + 12 + 4

21 + 20 + 31 + 16

41 + 47

88

88 / 8 = 11

Answer: 2/6 2/3 11/12

Step-by-step explanation: if you do the common denominator, you will find the numbers 2/6= 4/12 11/12=11/12 2/3=8/12. So your answer should be 2/6 11/12 2/3

Step-by-step explanation:

Completing the square is a method that is used for converting a quadratic expression of the form ax² + bx + c to the vertex form a(x - h)² + k. The most common application of completing the square is in solving a quadratic equation.

Completing the Square is a technique which can be used to find maximum or minimum values of quadratic functions. We can also use this technique to change or simplify the form of algebraic expressions. We can use it for solving quadratic equations.

[tex]x {}^{2} + 6 = - 2 \\ x {}^{2} + 6x + 9 = 7 \\ (x + 3) {}^{2} = 7[/tex]

The combination shows that the numbers of possible live card hands drawn without replacement from a standard deck of 52 playing cards is 2,598,960.

A permutation is the act of arranging the objects or numbers in order while combinations are the way of selecting the objects from a group of objects or collection such that the order of the objects does not matter.

Since the order does not matter, it means that each hand is a combination of five cards from a total of 52.

We use the formula for combinations and see that there are a total number of C( 52, 5 ) = 2,598,960 possible hands.

Learn more about permutations and combination on:

https://brainly.com/question/4658834

#SPJ1

Answer: 105 dollars

Step-by-step explanation:

Let's say that the original price x dollars, we can use the equation to find the original price.

80%x = 84

x = 105

Answer:

$105

Step-by-step explanation:

The multiplier is 0.8

To get the price after the discount,the original price was multiplied by 0.8(100 - 20 = 80% = 0.8

Therefore to obtain the original price from the price after the discount, we use reverse percentage:

$84 ÷ 0.8 = $105

The missing reasons for each of the given statements are respectively;

1) Substitution

2) Definition of a Straight angle because a straight angle is 180°.

3) Congruent Angles have equal measures

We are given that;

m∠1 = 90°

m∠1 + m∠2 = m∠5

∠3 ≅ ∠4

Statement 1; 90° + m∠2 + m∠4 = 180°

Reason 1; Substitution

Statement 2; m∠1 + m∠2 + m∠3 = 180°

Reason 2; Definition of a Straight angle because a straight angle is 180°.

Statement 3; m∠3 = m∠4

Reason 3; Congruent Angles have equal measures

Thus, the missing reasons for each of the given statements are respectively;

1) Substitution

2) Definition of a Straight angle because a straight angle is 180°.

3) Congruent Angles have equal measures

Read more about angles in a triangle at; https://brainly.com/question/12852445

#SPJ1

In mathematical notation, the set of integers less than -20 as follows:

{-21, -22, -23, -24, -25, ...}

The set of integers less than -20 is the set of all whole numbers that are smaller than -20. Integers include both positive and negative whole numbers, as well as zero.

In mathematical notation, we can represent the set of integers less than -20 as follows:

{-21, -22, -23, -24, -25, ...}

The set includes all numbers that are smaller than -20, going indefinitely in the negative direction. Each number in the set is obtained by subtracting 1 from the previous number in the set.

For example:

-21 is the integer immediately smaller than -20, so it is included in the set.

-22 is the next integer, smaller than -20, so it is also included in the set.

And this pattern continues indefinitely, encompassing all the integers less than -20.

To learn more on set click:

brainly.com/question/17201537

#SPJ3

Answer:

c

Step-by-step explanation:

Foreshortening is a technique used in perspective to create the illusion of an object receding strongly into the distance or background.

Foreshortening is a technique used to create the illusion of depth and three-dimensionality in a two-dimensional image.

Option B is the correct answer.

Foreshortening is a technique used in art to create the illusion of depth and three-dimensionality in a two-dimensional image.

It involves distorting the shapes of objects or figures to make them appear closer or farther away from the viewer, often by shortening the lengths of their features or changing the angle from which they are viewed.

Foreshortening is often used in drawing, painting, and other visual arts to create a sense of perspective and realism.

We have,

Foreshortening is a technique used to create the illusion of depth and three-dimensionality in a two-dimensional image.

It involves distorting the shapes of objects and figures to make them appear closer or farther away from the viewer, often by shortening the lengths of their features or changing the angle from which they are viewed.

Foreshortening can be used in drawing, painting, and other visual arts to create a sense of perspective and realism.

Thus,

Foreshortening is a technique used to create the illusion of depth and three-dimensionality in a two-dimensional image.

Learn more about foreshortening here:

https://brainly.com/question/29233426

#SPJ5

Answer:

Answer
5/9 is the dividend

Step-by-step explanation:

The number of tiles needed to cover the surface area of the box excluding the bottom is: 1,046 tiles.

The surface area of a box is the area surrounding all its faces. A box has 6 rectangular faces. Therefore, the total surface area of the box equals the sum of all 6 rectangular faces.

SA = 2(lw + lh + hw), where:

The image attached below shows the box Dmitri wants to cover. Since the bottom of the box would be excluded, therefore:

The surface area to be covered = surface area of the box - area of the bottom rectangular face

The surface area to be covered = 2(lw + lh + hw) - (l)(w)

l = 26

w = 15

h = 8

Substitute

The surface area to be covered = 2(l×w + lh + hw) - (l)(w) = 2·(15·26+8·26+8·15) - (26)(15) =

The surface area to be covered = 1436 - 390 = 1,046 cm

Area of one tile = 1 cm square

Number of tiles needed = 1,046/1

Number of tiles needed = 1,046 tiles.

Learn more about Surface Area of a Box on:

https://brainly.com/question/26161002

#SPJ1

The number of loaves of bread can the baker make with a 10 lb-bag of flour is 20 loaves of bread.

Ratio of flour to loaves of bread = 3 cups : 2 loaves

Number of loaves of bread can the baker make with a 10 lb-bag of flour

3 : 2 = 30 : x

3/2 = 30/x

3 × x = 2 × 30

3x = 60

x = 60/3

x = 20 loaves of bread

Therefore, the number of loaves of bread can the baker make with a 10 lb-bag of flour is 20 loaves of bread.

Learn more about loaves of bread:

https://brainly.com/question/19591550

#SPJ1

Answer:9[tex]a^{10}[/tex][tex]b^{-6}[/tex]=[tex]\frac{9a^{10} }{b^6}[/tex]

Step-by-step explanation:

Answer:

9*a^10*(1/(b^6))

Step-by-step explanation:

(-3a^5*b^-3)^2

(-3)^2 * (a^5)^2 * (b^-3)^2

9a^10*b^-6

9*a^10*(1/(b^6))

Solving the given logarithmic equation, it is found that the horn is 100 times more intense compared to the weakest sound heard to the human ear.

The equation is given by:

[tex]d = 10\log{\frac{p}{p_0}}[/tex]

In which:

In this problem, we have that d = 20, and we have to solve the logarithmic equation for p to find how many times more intense the sound is:

[tex]d = 10\log{\frac{p}{p_0}}[/tex]

[tex]20 = 10\log{\frac{p}{p_0}}[/tex]

[tex]\log{\frac{p}{p_0}} = 2[/tex]

The logarithm is inverse of the function [tex]10^x[/tex], hence we apply the function to both sides to find the ratio.

[tex]\frac{p}{p_0} = 10^2[/tex]

[tex]\frac{p}{p_0} = 100[/tex]

Hence, the horn is 100 times more intense compared to the weakest sound heard to the human ear.

More can be learned about logarithmic equations at https://brainly.com/question/236421

#SPJ1

Answer:

b. 30 m²

Step-by-step explanation:

find the area of the rectangle and triangle first

area of rectangle = length x height

aR = 10 x 6

aR = 60

area of triangle = base x height x 1/2

aT = 10 x 3 x 1/2

aT = 30

now, to find the area of the shaded area subtract the triangle from the rectangle

area = rectangle - triangle

a = 60 - 30

a = 30

[tex]\displaystyle \lim_{n\to \infty} ~~ \cfrac{5n^2}{7n^3-4}\qquad \implies \lim_{n\to \infty} ~~ \stackrel{\textit{using L'Hopital's rule}}{\cfrac{\frac{d}{dn}[5n^2]}{\frac{d}{dn}[7n^3-4]}}\implies \lim_{n\to \infty} ~~\cfrac{10n}{21n^2}\implies 0[/tex]

now, how do we get 0?

well, simple, hmmmm let me put a few values in

[tex]\cfrac{10(10)}{21(10)^2}\implies \cfrac{100}{2100}~~,~~ \cfrac{10(10000)}{21(10000)^2}\implies \cfrac{100000}{2100000000}~~,~~ ...[/tex]

in math lingo, on every iteration or change of the variable "n", the numerator is increasing but at a lower rate than the denominator, the denominator is increasing much more on every iteration, namely the denominator is moving faster and thus as "n" increases ever to infinity, the fraction becomes smaller and smaller and smaller, ever getting closer to 0.

Answer: 50 and 59

I divided 2950 by 25 because I knew it would somehow factor into that since it ends in 50. Then, I got 25 and 118. From there, I just divided 118 by 2 since I knew that it would end in a 9 and I multiplied 25 by 2. Not sure if this is really helpful, but you also try using a GCF calculator and look up all the factors of that number next time!

Answer:

○ [tex]y = \frac{1}{4}x - \frac{1}{2}[/tex]

Step-by-step explanation:

To find the equation of the line, let's first consider the points whose coordinates we have been given:

• (6, 1)

• (2, 0).

The point (2, 0) is what is called the x-intercept, which is the point where the line crosses the x-axis. This means that at this point, the y-coordinate of the line is 0.

Next, let's calculate the slope (gradient) of the line using the formula:

[tex]m = \frac{y_2 - y_1}{x_2 - x_1}[/tex]

where:

m = gradient,

[tex](x_2, y_2)[/tex] and [tex](x_1, x_2)[/tex] = points on the line.

Using the formula:

[tex]m = \frac{1 - 0}{6 - 2}[/tex]

⇒ [tex]m =\bf \frac{1}{4}[/tex]

Finally, now that we have two points on the line as well as the line's slope, we can use the following formula to find the equation of the line:

[tex]\boxed{y - y_1 = m(x - x_1)}[/tex]

You can use any of the points on the line as [tex]y_1[/tex] and [tex]x_1[/tex].

Using (2, 0):

[tex]y - 0 = \frac{1}{4}( x - 2)[/tex]

⇒ [tex]y = \frac{1}{4}x - \frac{1}{2}[/tex]

Therefore the equation of the line is [tex]y = \frac{1}{4}x - \frac{1}{2}[/tex].

Learn more about point-slope form at:

https://brainly.com/question/15143525

Answer:

47°

Step-by-step explanation:

If angles are complementary, that means those angles are added up to 90°.

Therefore,

43 + x = 90

Take 43 to the right side to make x as the subject.

x = 90 - 43

x = 47°

Note that a complementary angle adds up to 90 degrees.

In this problem, we get the equation:

43° + x = 90°

So, we need to find the value of x by doing:

90° – 43° = 47°

x = 47°

43° + 47° = 90°

We get the final result as:

x = 47°

Hope this helps :)

Answer:

Rounded to the nearest tenth would be 75.5 degrees

Step-by-step explanation:

The sum of the first 7 terms of the geometric series is 15.180

The formula for calculating the sum of geometric series is expressed according to the formula. below;

GM = a(1-r^n)/1-r

where

r is the common ratio

n is the number of terms

a is the first term

Given the following parameters from the sequence

a = 1/36

r = -3

n = 7

Substitute

S = (1/36)(1-(-3)^7)/1+3
S = 1/36(1-2187)/4
S = 15.180

Hence the sum of the first 7 terms of the geometric series is 15.180

Learn more on sum of geometric series here: https://brainly.com/question/24221513

#SPJ1

Using the t-distribution, it is found that since the p-value is greater than 0.01, there is no evidence that the new machine should be rejected at the 0.01 significance level.

At the null hypothesis, it is tested if the average is not less than 25, that is:

[tex]H_0: \mu \geq 25[/tex]

At the alternative hypothesis, it is tested if the average is less than 25, that is:

[tex]H_1: \mu < 25[/tex]

The test statistic is given by:

[tex]t = \frac{\overline{x} - \mu}{\frac{s}{\sqrt{n}}}[/tex]

The parameters are:

Considering the situation described, the values of the parameters are given as follows:

[tex]\overline{x} = 24.97, \mu = 25, s = 2.16, n = 10[/tex]

Hence the test statistic is:

[tex]t = \frac{\overline{x} - \mu}{\frac{s}{\sqrt{n}}}[/tex]

[tex]t = \frac{24.97 - 25}{\frac{2.16}{\sqrt{10}}}[/tex]

t = -0.04

Using a t-distribution calculator, for a left-tailed test, as we are testing if the mean is less than a value, with 10 - 1 = 9 df and t = -0.04, the p-value is of 0.4844.

Since the p-value is greater than 0.01, there is no evidence that the new machine should be rejected at the 0.01 significance level.

More can be learned about the t-distribution at https://brainly.com/question/13873630

#SPJ1

The function that is graphed is y = |x -2| + 3. The correct option is D. y = |x -2| + 3

From the question, we are to determine the function for the given graph

From the graph,

When x = 2, y = 3

The equation that satisfy this condition is

y = |x -2| + 3

NOTE: This function satisfies all the points on the graph

Hence, the function that is graphed is y = |x -2| + 3

Learn more on Absolute value graph here: https://brainly.com/question/17082317

#SPJ1

Answer: slope is 1/3

Step-by-step explanation: make a graph of y=1/3x+9

The probability that the person selected is 40 years old or younger is 0.61.

Probability determines the odds that a random event would happen. The probability the event occurs is 1 and the probability that the event does not occur is 0.

The more likely the event is to happen, the closer the probability value would be to 1. The less likely it is for the event not to happen, the closer the probability value would be to zero.

The probability that the person selected is 40 years old or younger = number of people 40 years or younger / total number of people at the movie theatre = (6 + 17 + 18 + 10 + 4 + 6) / (6 + 17 + 18 + 10 + 4 + 6 + 16 + 3 + 20)

61 / 100 = 0.61

To learn more about probability, please check: https://brainly.com/question/13234031

#SPJ1